Gallimard, as his relationship with Song becomes increasingly serious, seems to adopt more and more the stance of a "dominant" male expecting Song to be the "submissive" female, along with the corollary notion, in this context, that an Asian woman is supposed to be captivated by a white man. It's ironic because Gallimard from the start is apparently aware that these are cultural stereotypes, yet he still embraces them. Song encourages him to act in accordance with those cliches because it is part of his/her act; the role-playing insures that Gallimard will be duped completely by Song's masquerade, will therefore be completely trusting, and will reveal the political and military secrets the Chinese government is interested in.
Hwang uses, as the framework of these gender and racial assumptions, the plot of the play and opera Madame Butterfly. The story of M. Butterfly is a well-known cultural trope in the West, dealing as it does with an Asian woman who is seduced by an American naval officer, has a child by him, and then commits suicide when he abandons her. Gallimard links his relationship with Song to this story, calling her Butterfly and somehow accepting her story that she/he is pregnant by him. Throughout their affair, Song deliberately overplays the expected female and cultural submissiveness, referring to herself as Gallimard's "slave" and telling him that she has been taught to please him in a special "Chinese" way. It all works, of course, and Gallimard becomes the perfect dupe. When the deception is revealed, Gallimard eventually accepts the reversal of the roles implicit in their affair and kills himself.